ME 132 Summary–Intro and motivation of Feedback Control

• Following a reference (lectures, sec 1, pp1-3, sec 5)

• Rejecting a disturbance (lectures, sec 1, pp1-3 , sec 5)

• Increasing the speed-of-response (lectures, sec 1, pp1-3 , sec 5)

• Doing all of the above robustly to process variations (lectures, sec 1, pp1-3 , sec 5)

• Effect of sensor noise on process (lectures, sec 1, pp1-3 , sec 5)

• Block diagrams (sec 2, pg 9) and Simulink (sec 3 and lecture)

• P and PI controller for simplified cruise-control (sec 5, sec 8) & simplified stick-balancing (sec 2, page 10-12)

ME 132 Summary–Systems governed by ODEs (1st order and higher), PPT file

• Input/output (sec 6, sec 7)

• Definition of stability (sec 7, pg 59)

• Theorems of stability, location of roots, 1st, 2nd, 3rd, 4th order tests (sec 7, pg 62-64)

• Characterizing homogeneous solutions (sec 7.3)

• Step responses and sinusoidal steady-state responses (sec 7.5, sec 11, complex number identities)

• Effect of right-hand-side of ODE on the response to inputs (sec 9 and 10)

ME 132 Summary–Transfer function representation of systems governed by

ODEs (sec12)• Algebraic manipulations (derived by considering LDOs as

fundamental)

• Characterizing stability, steady-state gain, frequency-response, etc., in terms of the transfer function (lectures, Sec 13)

• Matlab @tf class (HW in Sec 12)

• Basic properties of and (lectures, HW in sec 11 and 12)

1s

22

2

2 nn

n

s

ME 132 Summary–Robustness Margins of Feedback Systems

• Gain margin

• Time delay margin

• Percentage-variation margin (“small-gain” theorem), (lectures)

• Phase Margin (lectures)

• Deriving Leffective for general problem (handout, HW 6 in Section 14)

–Controlling the position of an inertia using PI control with velocity feedback (PID control) (sec 23)

–Saturation and Anti-Windup Logic in controllers with Integral action (sec 15, HW #7 in sec 18)

ME 132 Summary–Systems governed by state-space models

• General form of state-equations (sec 3, sec 17, first 2 pages of sec 19)

• Rules for picking state variables in a few classes of systems (sec 16 and 17)

• Transfer function and Stability of a linear system of the form

–Linearizing a nonlinear system about an equilibrium point (sec 18)

• Equilibrium points

• Deriving the linearization

• Regulating a system near an equilibrium point with a feedback controller (hw #7 and #8 in sec 18)

)()()(

)()()(

tDutCxty

tButAxtx

ME 132 Summary– Intro and motivation of Feedback Control

• Following a reference (lectures, sec 1, pp1-3, sec 5)• Rejecting a disturbance (lectures, sec 1, pp1-3 , sec 5)• Increasing the speed-of-response (lectures, sec 1, pp1-3 , sec 5)• Doing all of the above robustly to process variations (lectures, sec 1, pp1-3 , sec 5)• Effect of sensor noise on process (lectures, sec 1, pp1-3 , sec 5)• Block diagrams(sec 2, pg 9) and Simulink (sec 3 and lecture)• P and PI controller for simplified cruise-control (sec 5, sec 8) & simplified stick-balancing (sec 2, page 10-12)

– Systems governed by ODEs (1st order and higher), PPT file• Input/output (sec 6, sec 7)• Definition of stability (sec 7, pg 59)• Theorems of stability, location of roots, 1st, 2nd, 3rd, 4th order tests (sec 7, pg 62-64)• Characterizing homogeneous solutions (sec 7.3)• Step responses and sinusoidal steady-state responses (sec 7.5, sec 11, complex number identities)• Effect of right-hand-side of ODE on the response to inputs (sec 9 and 10)

– Transfer function representation of systems governed by ODEs (sec12)• Algebraic manipulations (derived by considering LDOs as fundamental)• Characterizing stability, steady-state gain, frequency-response, etc., in terms of the transfer function (lectures, Sec 13)• Matlab @tf class (HW in Sec 12)• Basic properties of and (lectures, HW in section 12)

– Robustness Margins of Feedback Systems• Gain margin• Time delay margin• Percentage-variation margin (“small-gain” theorem), (lectures)• Phase Margin (lectures)• Deriving Leffective for general problem (handout, HW 6 in Section 14)

– Controlling the position of an inertia using PI control with velocity feedback (PID control) (sec 23)– Saturation and Anti-Windup Logic in controllers with Integral action (sec 15, HW #7 in sec 18)– Systems governed by state-space models

• General form of state-equations (sec 3, sec 17, first 2 pages of sec 19)• Rules for picking state variables in a few classes of systems (sec 16 and 17)• Transfer function and Stability of a linear system of the form

– Linearizing a nonlinear system about an equilibrium point (sec 18)• Equilibrium points• Deriving the linearization• Regulating a system near an equilibrium point with a feedback controller (hw #7 and #8 in sec 18)

1s

22

2

2 nn

n

s

)()()(

)()()(

tDutCxty

tButAxtx